The cast, according to the paper, will also include Tony Award winner Jeremy Irons, along with Russell Brand, Djimon Honsou, Felicity Jones, Alfred Molina, and Ben Whishaw, with Oscar winner Geoffrey Rush in negotiations to join the cast.
Taymor is best known as the director of The Lion King, for which she won the Tony Award, and is currently preparing a Broadway musical based on the comic-strip Spiderman. Her previous films include Titus, based on Shakespeare's Titus Andronicus, and Frida.
Mirren last appeared on Broadway in Dance of Death and is scheduled to return to the London stage next year in Phaedra. She won the Oscar for The Queen and has earned Emmy Awards for her work in Elizabeth I and Prime Suspect.